Fistula formation devices and methods therefor

ABSTRACT

Described here are devices, systems, and methods for forming a fistula between two blood vessels. Generally, the systems may comprise a first catheter and a second catheter, which may comprise one or more fistula-forming elements. The first and second catheters may comprise one or more magnets, which may be used to assist in bringing the first and catheters in closer proximity to facilitate fistula formation. In some variations, the magnet may have a plurality of magnetic domains each characterized by a magnetic flux vector, with the magnetic flux vectors of the magnet passing through a common magnetic origin.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application Ser.No. 61/953,723, filed on Mar. 14, 2014, and titled “FISTULA FORMULATIONDEVICES AND METHODS THEREFOR,” the content of which is herebyincorporated in its entirety.

FIELD

The current invention relates to devices and methods for forming afistula. The devices and methods may be used to form a fistula betweentwo blood vessels.

BACKGROUND OF THE INVENTION

A fistula is generally a passageway formed between two internal organs.Forming a fistula between two blood vessels can have one or morebeneficial functions. For example, the formation of a fistula between anartery and a vein may provide access to the vasculature for hemodialysispatients. Specifically, forming a fistula between an artery and a veinallows blood to flow quickly between the vessels while bypassing thecapillaries. In other instances, a fistula may be formed between twoveins to form a veno-venous fistula. Generally, fistula formationrequires surgical dissection of a target vein, and transecting andmoving the vein for surgical anastomosis to the artery. It may thereforebe useful to find improved ways to form a fistula between two bloodvessels.

BRIEF SUMMARY OF THE INVENTION

Described here are devices, systems, and methods for forming a fistula.In some variations, the systems described here may comprise a firstcatheter and a second catheter. The first catheter may comprise one ormore fistula-forming elements. The fistula-forming element may be anysuitable structure, such as an electrode. Additionally or alternatively,the second catheter may comprise one or more fistula-forming elements.The first and second catheters may comprise one or more magnets, whichmay be used to move the first and second catheters in closer proximityto facilitate fistula formation and/or to assist in aligning the firstand second catheters. In some variations, the magnets may havemagnetization patterns such that the magnetic field generated by themagnets is locally concentrated. In some of these variations, the firstcatheter may comprise a first magnet comprising a plurality of magneticdomains each having a magnetic flux vector. The plurality of magneticdomains of the first magnet may be configured such that the magneticflux vector of each magnetic domain intersects or passes through acommon magnetic origin. In some of these variations, the second cathetermay comprise a second magnet comprising a plurality of magnetic domainseach having a magnetic flux vector. The plurality of magnetic domains ofthe second magnet may be configured such that the magnetic flux vectorof each magnetic domain passes through a common magnetic origin.

In some variations of the systems described here, the system forcreating a fistula between two vessels comprises a first cathetercomprising a first magnet, and a second catheter comprising a secondmagnet, wherein at least one of the first and second catheters comprisesa fistula-forming element, and wherein the first magnet is characterizedby a first magnetization pattern comprising a first plurality ofmagnetic flux vectors, wherein each of the first plurality of magneticflux vectors intersects a first magnetic origin. In some of thesevariations, the first magnet comprises a longitudinal axis, and thefirst magnetic origin comprises a first line oriented substantiallyparallel to the longitudinal axis of the first magnet. In some of thesevariations, the first magnet has an approximately D-shaped cross-sectionand a longitudinal apex, and the magnetic origin is offset from thelongitudinal apex by between about 0.25 mm and about 0.5 mm. In some ofthese variations, the second magnet is characterized by a secondmagnetization pattern comprising a second plurality of magnetic fluxvectors, wherein each of the second plurality of magnetic flux vectorsintersects a second magnetic origin. In some of these variations, thefirst plurality of magnetic flux vectors is directed toward the firstmagnetic origin and the second plurality of magnetic flux vectors isdirected away from the second magnetic origin. In some of thesevariations, the first magnetic origin and the second magnetic origin atleast partially overlap. In some of these variations, the second magnetcomprises a longitudinal axis, and the second magnetic origin comprisesa second line oriented substantially parallel to the longitudinal axisof the second magnet. In some of these variations, the first magnetcomprises a longitudinal axis, and the first magnetic origin comprises afirst line oriented substantially perpendicular to the longitudinalaxis. In some variations, the first and second magnets are configuredsuch that when the rotational misalignment between the first and secondmagnets is greater than about 35 degrees, the attractive force betweenthe first and second magnets is less than about 50 percent of theattractive force when the rotational misalignment between the first andsecond magnets is zero. In some of these variations, the fistula-formingelement is an electrode.

In some variations of the systems described here, the system forcreating a fistula between two vessels comprises a first cathetercomprising a first magnet characterized at least partially with a firstplurality of magnetic flux vectors and a second catheter comprising asecond magnet, wherein at least one of the first and second catheterscomprises a fistula-forming element. In some of these variations, afirst portion of the first plurality of magnetic flux vectors isoriented in a first direction and a second portion of the firstplurality of magnetic flux vectors is oriented in a second directiondifferent from the first direction. In some of these variations, thesecond magnet is characterized at least partially with a secondplurality of magnetic flux vectors, wherein a first portion of thesecond plurality of magnetic flux vectors is oriented in a thirddirection and a second portion of the second plurality of magnetic fluxvectors is oriented in a fourth direction different from the thirddirection. In some of these variations, the first and second portions ofthe first plurality of magnetic flux vectors are directed toward a firstcommon locus, and the first and second portions of the second pluralityof magnetic flux vectors are directed away from a second common locus.In some of these variations, the first common locus and the secondcommon locus at least partially overlap. In some of these variations,the fistula-forming element is an electrode.

In some variations of the methods described here, the method of forminga fistula between a first blood vessel and a second blood vessel of apatient comprises advancing a first catheter into the first bloodvessel, wherein the first catheter comprises first magnet, advancing asecond catheter into the second blood vessel, wherein the secondcatheter comprises a second magnet, and wherein at least one of thefirst and second catheters comprises a fistula-forming element, movingthe first catheter toward the second catheter using the magnetic fieldproduced by the first magnet and second magnet, and forming a fistulawith the fistula-forming element, and wherein the first magnet ischaracterized by a first magnetization pattern comprising a firstplurality of magnetic flux vectors, wherein each of the first pluralityof magnetic flux vectors intersects a first magnetic origin, wherein thesecond magnet is characterized by a second magnetization patterncomprising a second plurality of magnetic flux vectors, wherein each ofthe second plurality of magnetic flux vectors intersects a secondmagnetic origin. In some of these variations, the first magnet comprisesa first longitudinal axis and the second magnet comprises a secondlongitudinal axis, and the first magnetic origin comprises a first lineoriented substantially parallel to the first longitudinal axis, and thesecond magnetic origin comprises a second line oriented substantiallyparallel to the second longitudinal axis. In some of these variations,the fistula-forming element is an electrode, and forming the fistulawith the fistula-forming element comprises ablating tissue with theelectrode. In some of these variations, the first blood vessel is a veinand the second blood vessel is an artery.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustrative depiction of a variation of a system describedhere comprising a first catheter and a second catheter.

FIG. 2A is an illustrative depiction of a magnet having an approximatelyD-shaped transverse cross-section and a magnetization pattern withparallel magnetic flux vectors. FIG. 2B is an illustrative depiction ofa magnet having an approximately D-shaped transverse cross-section and amagnet having non-parallel magnetic flux vectors.

FIGS. 3A-11B are illustrative depictions of variations of magnets eachhaving an approximately D-shaped transverse cross-section and amagnetization pattern suitable for use with the catheters describedhere.

FIG. 12A is an illustrative depiction of a magnet having anapproximately D-shaped transverse cross-section. FIG. 12B is anillustrative depiction of a longitudinal cross-section of the magnetdepicted in FIG. 12A having a magnetization pattern suitable for usewith the catheters described here.

FIG. 13A is an illustrative depiction of a pair of magnets havingapproximately D-shaped transverse cross-sections. FIG. 13B is anillustrative depiction of a transverse cross-section of a variation ofthe magnet pair depicted in FIG. 13A having magnetization patternssuitable for use with the catheters described here. FIG. 13C is anillustrative depiction of a cross-section of the magnetic field producedby the magnet pair of FIG. 13B.

FIG. 14A depicts the attractive force between two magnets suitable foruse with the catheters described here as a function of the distancebetween two magnets. FIG. 14B depicts the percentage increase in theattractive force between the magnets of FIG. 14A as a function of thedistance between the two magnets.

FIG. 15 is an illustrative depiction of a transverse cross-section of arotationally misaligned magnet pair.

FIG. 16 depicts the attractive force between first and second magnets asa function of the rotation angle of the first magnet relative to thesecond magnet.

FIGS. 17A and 18 depict the restoring torque between two magnetssuitable for use with the catheters described here as a function of therotational misalignment between the two magnets. FIG. 17B depicts thepercentage increase in the restoring torque between the magnets of FIG.17A as a function of the rotational misalignment between the twomagnets.

FIGS. 19A and 19B depict the percentage increase in restoring torquebetween two magnets suitable for use with the catheters described hereas a function of the rotational misalignment between the two magnets.

FIGS. 20A and 20B depict transverse cross-sections of demagnetizationprofiles of magnets having approximately D-shaped cross sections andhaving parallel magnetic flux vectors and non-parallel magnetic fluxvectors, respectively.

FIG. 21 is an illustrative depiction of a cross-section of a variationof a catheter pair comprising magnets described here.

FIG. 22A is an illustrative depiction of a magnet having anapproximately D-shaped transverse cross-section. FIGS. 22B and 22C areillustrative depictions of transverse cross-sections of variations ofthe magnet depicted in FIG. 22A having magnetization patterns suitablefor use with the catheters described here.

FIG. 23A is an illustrative depiction of a magnet having anapproximately D-shaped transverse cross-section. FIG. 23B is anillustrative depiction of a longitudinal cross-section of the magnetdepicted in FIG. 23A having a magnetization pattern suitable for usewith the catheters described here.

FIG. 24 is an illustrative depiction of a cross-section of a variationof a catheter pair comprising magnets described here.

FIG. 25A depicts a cross-section of a magnet, fixture, and coils used tomanufacture variations of magnets described here. FIG. 25B depicts aportion of the cross-section of FIG. 25A showing the magnetic fluxgenerated by the coils.

DETAILED DESCRIPTION OF THE INVENTION

Generally described here are systems, devices, and methods for forming afistula between blood vessels. The fistula may be, for example, anarteriovenous fistula between an artery and a vein, or a veno-venousfistula between two veins. Generally, to form a fistula between twoblood vessels, one or more catheters may be advanced in a minimallyinvasive fashion through the vasculature to a target fistula formationsite. Typically, a catheter may be placed in each of the two bloodvessels, such that a first catheter may be positioned in a first bloodvessel and a second catheter may be positioned in a second blood vessel.Accordingly, the systems described here may comprise a first catheterand a second catheter.

The first and second catheters may each have one or more magnets, whichmay be configured to aid in positioning and/or alignment of thecatheters. For example, in some instances the first catheter maycomprise one or more magnets which may be attracted to one or moremagnets of the second catheter, such that the magnets on the first andsecond catheters may act to pull the first and second catheters towardeach other and/or act to rotate the first and second catheters intorotational alignment. In some variations, the magnets may havemagnetization patterns generating non-uniform magnetic fields of focusedmagnetic strength. In some of these variations, the magnetizationpatterns may be configured to generate magnetic fields having thegreatest magnetic flux density or strength at a location between thefirst and second catheters when the catheters are positioned in twoblood vessels at a target fistula formation site.

Devices

Catheters

As mentioned above, the systems described here typically comprise afirst catheter and a second catheter. Any suitable catheter or cathetersmay be used with the systems described here to form the fistulas usingthe methods described here. For example, in some variations the systemmay comprise one or more of the catheters described in U.S. patentapplication Ser. No. 13/298,169, filed on Nov. 16, 2011 and titled“DEVICES AND METHODS FOR FORMING A FISTULA,” the contents of which arehereby incorporated by reference in their entirety. Generally, eachcatheter may have a proximal end, a distal end, and an intermediateportion connecting the proximal and distal ends. The proximal end maycomprise one or more adaptors or handles, which may be utilized to helpaid in advancement, positioning, and/or control of the catheter withinthe vasculature, and may further be used to actuate one or morecomponents of the catheter and/or introduce one or more fluids orsubstances into and/or through the catheter. The catheter may compriseone or more elements that may aid in fistula formation. For example, oneor more portions (e.g., the distal end and/or the intermediate portion)of the catheter may comprise one or more alignment elements, such asmagnets, that may help to align the catheter with another catheterpositioned in a related blood vessel, and/or help to bring the cathetersinto closer approximation, as will be described in more detail below. Asthe catheters are brought into closer approximation, the blood vesselswithin which the catheters are positioned may be brought into closerapproximation, which may aid in fistula formation. Additionally oralternatively, one or more portions (e.g., the distal end and/or anintermediate portion) of the catheter may comprise one or moremechanisms for forming a fistula.

The catheters may additionally comprise one or more lumens orpassageways extending at least partially along or through the catheter,but need not comprise these lumens or passageways. The lumens may beused to pass one or more guidewires, one or more drugs or fluids (e.g.,contrast agents, perfusion fluids), combinations thereof, or the like atleast partially along or through the catheter. The distal tip of thecatheter may be configured to aid in advancement of the catheter and/orconfigured to be atraumatic. In some variations, the tip may compriseone or more rapid exchange portions or other lumens for advancement ofthe catheter over a guidewire. In still other variations, the tipportion may have a guidewire attached to or otherwise integrally formedwith the catheter.

Additionally, in some variations the catheters may further comprise oneor more external expandable elements (e.g., a balloon, expandable cage,mesh, or the like) that may help position a catheter within a bloodvessel, but need not comprise one or more external expandable elements.Additionally or alternatively, the one or more expandable elements mayaffect the flow of blood through one or more blood vessels (e.g., bytemporarily occluding blood flow through the blood vessel, dilating oneor more portions of a blood vessel, constricting one or more portions ofa blood vessel, or the like). In some instances, one or more expandableelements may act to temporarily anchor a portion of the catheterrelative to a blood vessel. In variations in which a catheter comprisesone or more shape-changing elements, as will be described in more detailbelow, the use of an expandable element to temporarily anchor a portionof the catheter relative to a blood vessel may aid in altering the shapeof the catheter. It should be appreciated that the catheters describedhere may have any combination of the aforementioned elements.

FIG. 1 shows an illustrative variation of a catheter system that may beused to form a fistula between two vessels. As shown there, the systemmay comprise a first catheter (101) and a second catheter (103). Thefirst catheter (101) may comprise a catheter body (105), one or moremagnets (107), and a fistula-forming element (109) which may beactivated to form a fistula. In some variations, the fistula-formingelement (109) may be advanced within the catheter body (105) to projectout of an opening (111) in the catheter body (105). In some variations,the first catheter (101) may comprise a housing (113), which may helpprotect other components of the first catheter (101) during fistulaformation. For example, when the fistula-forming element (109) comprisesan electrode configured to ablate tissue, the housing (113) may compriseone or more insulating materials which may shield or otherwise protectone or more components of the first catheter (101) from heat that may begenerated by the electrode during use.

As shown in FIG. 1, a second catheter (103) may also comprise a catheterbody (115) and one or more magnets (107). In variations in which thefirst catheter (101) comprises a fistula-forming element (109)configured to project out of the catheter body (105) of the firstcatheter (101), such as the variation depicted in FIG. 1, the catheterbody (115) of the second catheter (103) may comprise a recess (117)therein, which may be configured to receive the fistula-forming element(109) as it passes through tissue during fistula formation. In some ofthese variations, the recess (117) may be coated by an insulatingmaterial (not shown), which may be configured to protect one or morecomponents of the second catheter (103) from being damaged by thefistula-forming element (109) (e.g., the insulating material may shieldone or more components of the second catheter (103) from heat that maybe generated by the fistula-forming element (109)). While the secondcatheter (103) is shown in FIG. 1 as having a recess (117), it shouldalso be appreciated that in some variations the second catheter (103)may not comprise a recess (117). In some variations, the second cathetermay comprise a fistula-forming element (not shown) such that the firstcatheter (101) and/or the second catheter (103) comprises afistula-forming element, as will be described in detail below.

Fistula-Forming Elements

As mentioned above, the catheters described here may comprise one ormore elements for forming a fistula. The fistula-forming element maycomprise any element capable of forming a fistula between two vessels,such as those elements described in U.S. patent application Ser. No.13/298,169, which was previously incorporated by reference in itsentirety. For example, the fistula-forming element may comprise one ormore electrical mechanisms (e.g., electrodes or electrocauterymechanisms). A catheter may have any suitable number (e.g., zero, one,two, three, or four or more) and combination of these fistula-formingelements. The fistula-forming elements may be located in or on anysuitable portion of the catheter (e.g., the distal end, an intermediateportion, or combinations thereof). In variations in which a cathetercomprises two or more fistula-forming elements, multiple fistula-formingelements may be used to create multiple fistulas, either simultaneouslyor sequentially. In other variations, multiple fistula-forming elementsmay interact to form a single fistula.

In variations in which a system comprising multiple catheters is used tocreate a fistula between two blood vessels, each catheter may comprise afistula-forming element, but need not. Indeed, in some of thesevariations, only one catheter may comprise a fistula-forming element. Insome of these instances, a second catheter that lacks a fistula-formingelement may still help align the catheters and/or bring the bloodvessels into apposition, but might not directly contribute to tissueremoval. In variations in which multiple catheters each comprise afistula-forming element, the catheters may have complementaryfistula-forming elements. For example, in variations in which two ormore catheters each comprise an electrode, one catheter may comprise anelectrode that acts as an active electrode, while another catheter maycomprise an electrode that acts as a passive or ground electrode.

In some variations of the catheters described here, a catheter maycomprise one or more electrodes for use in forming a fistula. Such anelectrode may be used to ablate or otherwise remove the tissue incontact with the electrode in order to form the fistula. If afistula-forming element comprises an electrode, the electrode may, forexample, be configured as described in U.S. patent application Ser. No.13/298,169, which was previously incorporated by reference in itsentirety.

In the embodiment shown in FIG. 1, the fistula-forming element (109) ofthe first catheter (101) comprises an electrode. The electrode may beselectively moved from a position in which the electrode is retained orotherwise held in the catheter body (105) to a position in which theelectrode extends away from the catheter body (105) (e.g., through theopening (111)), and the electrode may also be selectively moved back toa retracted/low-profile position (either the same position as theprevious retracted position, or a different position) following ablationof tissue. This may allow the electrode to be maintained in alow-profile configuration during positioning of the catheter. In somevariations, the electrode may be biased toward an extended position whennot otherwise restrained by the catheter body (105).

Magnets

As mentioned above, the first and second catheters of the systemsdescribed here may comprise one or more magnets. Generally, the magnetsmay be configured to be attracted to one or more magnetic fields (e.g.,produced by one or more magnets of another catheter). The magnets mayhelp to align or otherwise reposition the catheters when placed in thevasculature. In some instances, a system may comprise first and secondcatheters each having one or more magnets, such that magnets of thefirst catheter may be attracted to magnets of the second catheter tobring the catheters in closer approximation. In other instances, one ormore magnets may help to ensure that one or more catheters are in properaxial and/or rotational alignment relative to another catheter orcatheters, such as described in further detail in U.S. patentapplication Ser. No. 13/298,169, which was previously incorporated byreference in its entirety. Such axial and/or rotational alignment ofcatheters may also facilitate alignment of one or more fistula-formingelements relative to a target fistula-formation site.

The magnets described here may be permanent magnets comprising one ormore hard magnetic materials, such as but not limited to alloys of rareearth elements (e.g., samarium-cobalt magnets or neodymium magnets, suchas N52 magnets) or alnico. In some variations, the magnets may compriseanisotropic magnets; in other variations, the magnets may compriseisotropic magnetics. In some variations, the magnets may be formed fromcompressed powder, as will be described in more detail below. In somevariations, a portion of the magnets (e.g., a permeable backing) maycomprise one or more soft magnetic materials, such as but not limited toiron, cobalt, nickel, or ferrite.

It should be appreciated that while the systems primarily described herecomprise a first catheter and a second catheter each comprising one ormore permanent magnets, in other variations either the first or secondcatheter may comprise ferromagnetic elements (i.e., elements attractedto but not generating a permanent magnetic field). For example, in somevariations, the first catheter may include only one or moreferromagnetic elements while the second catheter comprises one or morepermanent magnets. In other variations, the second catheter may includeonly one or more ferromagnetic elements while the first cathetercomprises one or more permanent magnets. However, in other variations,one or both of the first and second catheters may include any suitablecombination of ferromagnetic, permanent, and/or other suitable kinds ofmagnets.

In variations in which the catheters of the systems described herecomprise one or more magnets, each catheter may comprise any number ofindividual magnets (e.g., one, two, three, four, five, six, seven, oreight or more, etc.). In variations in which a catheter comprises aplurality of magnets, these magnets may be grouped into one or moremagnet arrays. The magnets may be located inside and/or outside of acatheter body. The magnets may be positioned anywhere along the lengthof the catheter. In some variations in which the system comprises afirst catheter having a fistula-forming element (such as the firstcatheter (101) shown in FIG. 1), the first catheter may comprise one ormore magnets proximal to a fistula-forming element. Additionally oralternatively, the first catheter may comprise one or more magnetsdistal to a fistula-forming element. In some variations in which asystem comprises a second catheter comprising a fistula-forming element,the second catheter may comprise one or more magnets proximal to thefistula-forming element. Additionally or alternatively, in variations inwhich the second catheter comprises a fistula-forming element, thesecond catheter may comprise one or more magnets distal to thefistula-forming element. In variations in which both the first andsecond catheters comprise one or more magnets, each magnet or array inthe first catheter may be configured to align with one or more magnetsin a second catheter. Each magnet may be fixed in or on a catheter byany suitable method. For example, in some variations one or more magnetsmay be embedded in, adhered to, or friction-fit within a catheter.

Generally, the dimensions of the magnets may be constrained by the sizeof the catheters carrying the magnets, which in turn may be constrainedby the anatomical dimensions of the selected blood vessels through whichthe catheters described here may be advanced. For example, if thecatheter is to be advanced through a blood vessel having an internaldiameter of about 3 mm, it may be desirable to configure any magnet tobe less than about 3 mm at the widest part of its cross-section, toreduce the risk of injury to vessel walls during advancement andmanipulation of the catheter. Each magnet may have any suitable length(e.g., about 5 mm, about 10 mm, about 15 mm, about 20 mm, or the like),although it should be appreciated that in some instances longer magnetsmay limit the flexibility of the catheter to maneuver through tissue.

In variations in which two catheters each comprise one or more magnets,the magnets of the catheters may produce an attractive force between thecatheters, which may act to pull the catheters into closerapproximation. Once the first and second catheters have been positioned,the attractive force may also act to maintain the relative positions ofthe catheters. When the first and second catheters are placed inrespective blood vessels, however, tissue positioned between the bloodvessels and/or limited compliance of the blood vessels may limit theextent to which the magnets of the first and second catheters bring thefirst and second catheters toward each other.

“Focused” Magnets

The extent to which the first and second catheters may be brought towardand/or rotationally aligned with each other may be improved by utilizingmagnets having particular magnetic fields of focused strength. Such“focused” magnets have a magnetic field with at least one region inwhich magnetic strength is higher than surrounding regions, as comparedto “non-focused” magnets (described in more detail below). Inparticular, the magnetic field patterns of the respective magnets on thefirst and second catheters may be designedly focused in order to urgethe first and second catheters toward a desired arrangement with oneanother, with more force than that provided by magnets with uniformmagnetic fields. For example, when the first and second catheters arewithin respective blood vessels near a target fistula formation site,the magnetic field strength of the focused magnets may be focused at acommon location between the first and second catheters, thereby urgingthe first and second catheters into closer approximation with anincreased attractive force as compared to non-focused magnets of thesame size. Thus, the catheters may be better able to displace tissuebetween the blood vessels or overcome limited vessel compliance in orderto help the first and second catheters move toward each other.

Because the catheters described herein may be advanced into the body,the patient's anatomy and other factors may place constraints on thedimensions of the catheters and the magnets that ordinarily would limitthe amount of attractive force provided by magnets on the catheters.Accordingly, in instances in which the size of catheters and the magnetsare physically limited to a particular size, the inclusion of focusedmagnets having focused magnetic fields may facilitate an additionalincrease in attractive force between two catheters comprising suchmagnets, without exceeding dimensional constraints. This may, forexample, allow the catheters to overcome additional compliance and/orresistance (e.g., due to tissue between the vessels) to help bring thecatheters and/or blood vessels into apposition. Alternatively, focusedmagnets having focused magnetic fields may allow the catheter size to bedecreased while maintaining a certain attractive force between thecatheters. For example, in some instances, the catheter size may be ableto be decreased from 5 Fr to 4 Fr while maintaining the same attractiveforce between the catheters; in other instances, the catheter size maybe able to be decreased from 6 Fr to 5 Fr while maintaining the sameattractive force between the catheters.

Compared to a non-focused magnet, a focused magnet may create a magneticfield of focused strength as a result of having a specializedmagnetization pattern. FIG. 2A illustrates the magnetization pattern ofa cross-section of an exemplary non-focused magnet (204), and FIG. 2Billustrates the specialized magnetization pattern of a cross-section ofan exemplary focused magnet (205). Each magnet includes a plurality ofregions, or magnetic domains. Each magnetic domain has a uniformmagnetization within itself, and a respective polarity direction that isrepresented by a magnetic flux vector (201). The difference between anon-focused magnet and a focused magnet is illustrated by the differentmagnetization pattern of their magnetic domains. As shown in FIG. 2A, anon-focused magnet (204) has a magnetization pattern characterized withparallel magnetic flux vectors (201) that are oriented in the samedirection (shown in FIG. 2A as directed upward). In contrast, as shownin FIG. 2B, a focused magnet (205) has a magnetization patterncharacterized with non-parallel magnetic flux vectors (201) forming aspecialized magnetization pattern in which each magnetic flux vector(201) intersects or passes through a particular common location orcommon locus called the magnetic origin (203). Put another way, afocused magnet has a magnetic origin located a measurable distance(i.e., a non-infinite distance) from the magnet (hereinafter referred toas “magnetization radius”) where magnetic flux vectors (201) meet, whilea non-focused magnet has a magnetic origin located an infinite distanceaway from the magnet (i.e., a non-focused magnet has a magnetizationradius of infinity). Accordingly, the magnetization pattern concentratesor focuses magnetic flux at the magnetic origin, such that the magneticfield strength of the magnet is maximum at the magnetic origin (203). Inother words, a focused magnet with such a focused magnetic fieldgenerates a greater magnetic flux density, or greater magnetic force, atthe magnetic origin than that otherwise generated by a non-focusedmagnet of similar dimensions and material type.

In some variations, as shown for example in FIGS. 3A and 3B, a focusedmagnet may have a longitudinal magnetic origin (shown as line (303) inFIG. 3A) in the form of a line parallel to a longitudinal axis of themagnet (shown as line (304) in FIG. 3A). For example, a focused magnetmay have a longitudinal magnetic origin in the form of a line translatedfrom the longitudinal axis of the magnet (i.e., oriented parallel to andlocated offset from the longitudinal axis of the magnet). In thesevariations, as shown in FIGS. 3A-11B (discussed in more detail below),the magnetization pattern of each transverse cross-section of the magnetmay include magnetic flux vectors that commonly pass through a singlepoint along the longitudinal magnetic origin, where that single point isin the plane of the transverse cross-section. In other words, themagnetic field of each transverse “slice” of the focused magnet may berepresented by a respective set of magnetic flux vectors that intersectat a respective single common point, and the series of common pointsalong all “slices” form the longitudinal magnetic origin. As such, themagnetic force produced along the longitudinal magnetic origin of afocused magnet is greater than the magnetic force produced by anon-focused magnet. In some of these variations, the line may be locatedalong a central longitudinal plane of the magnet.

FIGS. 3A-11B depict exemplary variations of focused magnets withlongitudinal magnetic origins. Each of FIGS. 3A-11A depicts a focusedmagnet having an approximately D-shaped transverse cross-section (shownin FIGS. 3B-11B, respectively) and a longitudinal apex (302) thatextends longitudinally along the apex of convexity of the magnet,substantially parallel to longitudinal axis (304). Each of the magnetsof FIGS. 3A-11B comprises a plurality of magnetic domains, where eachmagnetic domain may be represented by a respective magnetic flux vector(each represented by an arrow (301)). When fully extended within itsplane, each magnetic flux vector (301) passes through a point on thelongitudinal magnetic origin (303). In some variations, as shown inFIGS. 3A-11B, a focused magnet may have a longitudinal magnetic origin(303) that is translated or offset by any suitable distance (d) (notlabeled in FIGS. 3A and 3B) from the longitudinal apex (302) of themagnet (i.e., offset by the magnetization radius). In some variations,the magnetization radius may be about 0 mm to about 6 mm, about 0.1 mmto about 5 mm, about 0.2 mm to about 4 mm, about 0.3 mm to about 3 mm,about 0.4 mm to about 2 mm, about 0.5 mm to about 1 mm, or more thanabout 6 mm. Generally speaking, as the magnetization radius is increasedand the magnetic origin is more distant from a focused magnet, themagnetic flux vectors of the magnet become less angled (i.e., becomecloser to approximating parallel orientations). For example, FIG. 3Bdepicts a transverse cross-section of a magnet (305) having amagnetization radius of about 0 mm (i.e., a longitudinal magnetic origin(depicted by circle (303)) located substantially incident or collinearwith the longitudinal apex (302) of the magnet (305)). FIG. 4B depicts atransverse cross-section of a magnet (307) having a magnetization radiusof about 0.25 mm (i.e., a longitudinal magnetic origin (303) locatedabout 0.25 mm from the longitudinal apex (302) of the magnet (307)).FIG. 5B depicts a transverse cross-section of a magnet (309) having amagnetization radius of about 0.5 mm (i.e., a longitudinal magneticorigin (303) about 0.5 mm from the longitudinal apex (302) of the magnet(309)). FIG. 6B depicts a transverse cross-section of a magnet (311)having a magnetization radius of about 0.75 mm (i.e., a longitudinalmagnetic origin (303) about 0.75 mm from the longitudinal apex (302) ofthe magnet (311)). FIG. 7B depicts a transverse cross-section of amagnet (313) having a magnetization radius of about 1 mm (i.e., alongitudinal magnetic origin (303) about 1 mm from the longitudinal apex(302) of the magnet (313)). FIG. 8B depicts a transverse cross-sectionof a magnet (315) having a magnetization radius of about 2 mm (i.e., alongitudinal magnetic origin (303) about 2 mm from the longitudinal apex(302) of the magnet (315)). FIG. 9B depicts a transverse cross-sectionof a magnet (317) having a magnetization radius of about 4 mm (i.e., alongitudinal magnetic origin (303) about 4 mm from the longitudinal apex(302) of the magnet (317)).

While FIGS. 3A-11B show magnets comprising a plurality of magneticdomains with magnetic flux vectors passing through and oriented towardthe magnetic origin, in other variations, as shown for example in FIGS.10A-10B and 11A-11B, the magnets may comprise a plurality of magneticdomains with magnetic flux vectors intersecting (when extended) themagnetic origin and oriented away from the magnetic origin. For example,FIG. 10B depicts a transverse cross-section of a magnet (319) having amagnetization radius of about 0 mm (i.e., a magnetic origin (303)located substantially incident or collinear with the longitudinal apex(302) of the magnet (319), where each magnetic flux vector (301)intersects the magnetic origin (303) and is oriented away from themagnetic origin (303). FIG. 11B depicts a transverse cross-section of amagnet (321) having a magnetization radius of about 1 mm (i.e., amagnetic origin (303) located about 1 mm from the longitudinal apex(302) of the magnet (321)), where each magnetic flux vector (301)intersects the magnetic origin (303) and is oriented away from themagnetic origin (303). Furthermore, while FIGS. 3B-11B depict a singletransverse cross-section of each magnet, it should be appreciated thatwhen the magnetic origin is a longitudinal magnetic origin, some or alltransverse cross-sections of the magnet may have substantially similarmagnetization patterns, such that the magnetic domains in at least sometransverse cross-sections of the magnet are represented by substantiallysimilar configurations of magnetic flux vectors.

In other variations, as shown for example in FIG. 12A, a focused magnetmay have a transverse magnetic origin (shown as line (403) in FIG. 3A)in the form of a line that is approximately perpendicular to alongitudinal axis (shown as line (403) in FIG. 12A). In thesevariations, as shown in FIG. 12B (discussed in more detail below), themagnetization pattern of each longitudinal cross-section of the magnetmay include magnetic flux vectors that commonly pass through a singlepoint along the transverse magnetic origin, where that single point isin the plane of the longitudinal cross-section. In other words, themagnetic field of each longitudinal “slice” of the focused magnet may berepresented by a respective set of magnetic flux vectors that intersectat a respective single common point, and the series of common pointsalong all “slices” form the transverse magnetic origin. As such, themagnetic force produced along the transverse magnetic origin of afocused magnet is greater than the magnetic force produced by anon-focused magnet of similar size and material type. In some of thesevariations, the line may be located along a central transverse plane ofthe magnet.

FIG. 12A depicts an exemplary variation of a focused magnet with atransverse magnetic origin (403). In particular, FIG. 12A depicts afocused magnet (405) having an approximately D-shaped transversecross-section and a longitudinal apex (402) that extends longitudinallyalong the apex of convexity of the magnet (405). FIG. 12B depicts alongitudinal cross-sectional view of a focused magnet similar to thatdepicted in FIG. 12A, and a transverse magnetic origin (403). That is,the magnet (405) of FIG. 12B may comprise a plurality of magneticdomains, where each magnetic domain may be represented by a respectivemagnetic flux vector (each represented by an arrow (401)). When fullyextended, each magnetic flux vector (401) passes through a point on thetransverse magnetic origin (depicted by circle (403)). As shown in FIGS.12A and 12B, the transverse magnetic origin (403) may be translated oroffset by any suitable distance (d) from the longitudinal apex (402) ofthe magnet, such as about 0 mm to about 6 mm, about 0.1 mm to about 5mm, about 0.2 mm to about 4 mm, about 0.3 mm to about 3 mm, about 0.4 mmto about 2 mm, about 0.5 mm to about 1 mm, or more than about 6 mm. Forexample, FIG. 12B depicts a transverse cross-section of a magnet (405)having a magnetic origin (depicted by circle (403)) located about 4 mmfrom the longitudinal apex (402) of the magnet (405). Generallyspeaking, as the magnetization radius is increased and the magneticorigin is more distant from a focused magnet, the magnetic flux vectorsof the magnet become less angled (i.e., become closer to approximatingparallel orientations).

While FIG. 12B depicts a magnet comprising a plurality of magneticdomains with magnetic flux vectors passing through and oriented towardthe magnetic origin, in other variations, the magnets may comprise aplurality of magnetic domains with magnetic flux vectors intersecting(when extended) the magnetic origin and oriented away from the magneticorigin. Furthermore, while FIG. 12B depicts a single longitudinalcross-section of the magnet (405), it should be appreciated that whenthe magnetic origin comprises a transverse magnetic origin, some or alllongitudinal cross-sections of the magnet may have the samemagnetization pattern, such that the magnetic domains in at least somelongitudinal cross-sections of the magnet are represented by thesubstantially similar configurations of magnetic flux vectors.

In yet other variations, a focused magnet may have a magnetic origin inthe form of a single point. As such, the magnetic force produced at thispoint may be greater than the magnetic force produced by a non-focusedmagnet of similar size and material type. In these variations, eachmagnetic flux vector of the magnet may pass through the single magneticorigin point. In some of these variations, the single magnetic originpoint may be located along a line formed by the intersection of acentral transverse plane of the magnet and a central longitudinal planeof the magnet.

It should also be appreciated that while FIGS. 2A-11B depict magnetshaving approximately D-shaped transverse cross-sections, in othervariations, the magnets may have other shapes. For example, in othervariations the magnets may be cylindrical, semi-cylindrical, or have across-section that is C-shaped (i.e., a D-shape or semi-cylindricalshape comprising a channel on the flat surface), rectangular, square,triangular, trapezoidal, ovoid, elliptical, or an n^(th)-order polygon,or the like.

In some variations, a first catheter may comprise a first magnetcomprising a plurality of magnetic domains each having a magnetic fluxvector oriented toward a magnetic origin, and a second catheter maycomprise a second magnet comprising a plurality of magnetic domains eachhaving a magnetic flux vector oriented away from a magnetic origin. Forexample, FIG. 13A depicts a first magnet (1301) having a longitudinalapex (1302) and second magnet (1303) having a longitudinal apex (1304).First magnet (1301) and second magnet (1303) may be located in first andsecond catheters (not shown), respectively. As shown in FIG. 13B, thefirst magnet (1301) may comprise a plurality of magnetic domains eachhaving a magnetic flux vector (each depicted by an arrow (1305)) passingthrough and directed toward a longitudinal magnetic origin (1309)located about 1 mm from the longitudinal apex (1302) of the first magnet(1301). The second magnet (1303) may comprise a plurality of magneticdomains each having a magnetic flux vector (each depicted by an arrow(1307)) intersecting (when extended) a longitudinal magnetic origin(1311) and directed away from the longitudinal magnetic origin (1311),where the longitudinal magnetic origin (1311) is located about 1 mm fromthe longitudinal apex (1304) of the second magnet (1303).

When the first magnet (1301) and second magnet (1303) are positionedsuch that the convex side of the first magnet (1301) faces the convexside of the second magnet (1303) and the magnetic origins (1309) and(1311) are approaching the at least partial overlap or superpositiondepicted in FIGS. 13A and 13B, the magnetic field produced by the firstmagnet (1301) may attract the second magnet (1303) toward the firstmagnet (1301), while the magnetic field produced by the second magnet(1303) may in turn attract the first magnet (1301) toward the secondmagnet (1303). In some variations, the first magnet (1301) and thesecond magnet (1303) are configured such that their respective magneticorigins (1309) and (1311), respectively, are located in the center ofthe “air gap” distance between the magnets. FIG. 13C depicts theresulting magnetic field produced by the first magnet (1301) and secondmagnet (1303) when they are located about 2 mm away from each other. Asillustrated in FIG. 13C, the greatest flux density is located in thearea between the two magnets.

As described above, in some variations, a first catheter comprises afirst focused magnet having a plurality of magnetic domains each havinga magnetic flux vector oriented toward a magnetic origin, and a secondcatheter comprises a second focused magnet having a plurality ofmagnetic domains each having a magnetic flux vector oriented away from amagnetic origin. In such variations, the attractive force between thefirst magnet and the second magnet may in some instances be greater thanthe attractive force between two non-focused magnets (i.e., each havingparallel magnetic flux vectors, with a magnetization radii of infinity).The increased attractive force between the first focused magnet and thesecond focused magnet may depend on the distance between the first andsecond focused magnets, the magnetic radii of the first and secondfocused magnets, and/or the rotational alignment of the first and secondfocused magnets.

Magnets—Attractive Force

Different configurations of pairs of magnets may result in differentamounts of attractive force. FIGS. 14A and 14B depict the attractiveforce between a pair of first and second magnets, as compared acrossdifferent kinds of magnet pairs. In particular, FIG. 14A depicts theattractive force between first and second non-focused magnets as afunction of the distance between the two magnets (the “air gap”). FIG.14A also depicts the attractive force between a pair of first and secondfocused magnets as a function of the “air gap,” for different pairs offocused magnets having a range of magnetic radii. The non-focused andfocused magnets are N52 NdFeB magnets, each having a D-shaped transversecross-section, a diameter of 0.0675 inches, a longitudinal length of0.25 inches, and a distance from the longitudinal apex to the flatsurface of the magnet of 0.044 inches. The focused magnets have alongitudinal magnetic origin. FIG. 14B depicts a comparison ofattractive force between a pair of non-focused magnets and betweendifferent pairs of focused magnets similar to that depicted in FIG. 14A,but FIG. 14B depicts this comparison in terms of percentage increase inattractive force as a function of “air gap.”

As can be seen in FIGS. 14A-14B, in some instances when the first andsecond focused magnets are in close proximity, both absolute andrelative attractive force increase with decreasing magnetic radii of thefirst and second focused magnets. For example, when the air gap is about0 mm (i.e., the magnets are touching or nearly touching), the attractiveforce between focused magnets having magnetic radii of about zero isabout 157% greater than between the attractive force between non-focusedmagnets; the attractive force between focused magnets having magneticradii of about 0.25 mm is about 104% greater than the attractive forcebetween non-focused magnets; the attractive force between focusedmagnets having magnetic radii of about 0.5 mm is about 76% greater thanthe attractive force between nonmagnetic magnets; the attractive forcebetween focused magnets having magnetic radii of about 0.75 mm is about60% greater than that between non-focused magnets; the attractive forcebetween focused magnets having magnetic radii of about 1 mm is about 50%greater than that between non-focused magnets; the attractive forcebetween focused magnets having magnetic radii of about 2 mm is about 30%greater than that between non-focused magnets; and the attractive forcebetween focused magnets having magnetic radii of about 4 mm is about 16%greater than that between non-focused magnets. Because the attractiveforce between focused magnets is a function of at least bothmagnetization radius and distance (“air gap”) between the magnets, itmay be desirable to have first and second magnets having magnetic radiithat maximize the attractive force between the two magnets when they area particular distance apart. More specifically, when the first andsecond magnets are respectively located in first and second cathetersthat may be used to create a fistula, the magnets may be located about 2mm to about 4 mm apart, such as during catheter delivery toward a targetfistula location. As the attractive force between the magnets pulls thecatheters and magnets in closer approximation (as described in moredetail below), the magnets may move to be less than about 0.5 mm apart.Therefore, in some variations, it may be desirable for the first andsecond magnets to have magnetic radii of approximately about 0.25 mm toabout 0.5 mm or order to increase the attractive force through a rangeof air gaps from less than about 0.5 mm through about 2-4 mm. In othervariations, it may be desirable for the first and second magnets to havemagnetic radii of approximately about 0 mm to about 6 mm, about 0.1 mmto about 5 mm, about 0.2 mm to about 4 mm, about 0.3 mm to about 3 mm,about 0.4 mm to about 2 mm, about 0.5 mm to about 1 mm, or more thanabout 6 mm. It should be appreciated that while the exemplary attractiveforce shown in FIGS. 14A-14B is for multiple pairs of first and secondmagnets having magnetic radii identical to one another, in othervariations, the first and second magnets may have magnetic radiidifferent from one another.

As mentioned briefly above, the amount of attractive force between twomagnets may depend at least partially on the relative rotationalalignment of the first and second magnets. For example, as shown in FIG.15, a first magnet (1501) and a second magnet (1503) may be approximateeach other and rotated relative to one another by an angle φ (referredto hereinafter as the “rotational misalignment”). First and secondmagnets (1501) and (1503) may be non-focused magnets or focused magnets.The attractive force between the first and second magnets (1501) and(1503) is depicted as Fy. FIG. 16 depicts a comparison of the attractiveforce between a pair of non-focused magnets and the attractive forcebetween a pair of focused magnets having magnetization radii of about 0mm, as a function of rotational misalignment. The magnets within eachmagnet pair of FIG. 16 are separated by a distance of about 1 mm, andare N52 NdFeB magnets each having a D-shaped transverse cross-section, adiameter of 0.0675 inches, a longitudinal length of 0.25 inches, and adistance from the apex to the flat surface of the magnet of 0.044inches. As shown in FIG. 16, the attractive force is greatest when thefirst and second magnets are rotationally aligned (i.e., when therotational misalignment is zero). The attractive force decreases as therotational misalignment increases. At low rotational misalignments(e.g., in the example here below about 35 degrees), the attractive forceis greater between focused magnets than between non-focused magnets.

In contrast, however, at high rotational misalignments (e.g., in theexample here, above about 35 degrees), the attractive force betweenfocused magnets is less than that between non-focused magnets. Onepractical effect of this relationship is that two focused magnets,separated by a given distance, have a lower tendency to attract oneanother at high rotational misalignment, compared to two non-focusedmagnets separated by the same distance and similarly rotationallymisaligned. Low attractive force between significantly rotationallymisaligned magnets may be desirable to prevent the magnets from movingtoward each other when significantly misaligned. When the magnets arelocated within catheters as described herein, this may prevent the firstand second catheters from moving into closer approximation when afistula-forming element of a first catheter (such as fistula-formingelement (109) described above) is not properly aligned with a recess ofa second catheter configured to receive the fistula-forming element(such as recess (117) described above).

Thus, focused magnets may have higher attractive force at low rotationalmisalignment and lower attractive force at high rotational misalignment,as compared to non-focused magnets. Put another way, the rate ofdecrease in attractive force as a function of rotational misalignment(i.e., the slope of the curves in FIG. 16) may increase with decreasingmagnetic radii of the first and second magnets. For example, in theexample of FIG. 16, the attractive force between non-focused magnetsdecreases by about 50% when rotational misalignment is about 50 degrees,relative to its maximum at 0 degrees of rotational misalignment. Incontrast, the attractive force between focused magnets with 0 mmmagnetization radii decreases by about 50% when rotational misalignmentreaches about 35 degrees, relative to its maximum at 0 degrees ofrotational misalignment.

Magnets—Restoring Torque

Different magnet pairs may have different torque urging the magnets torotationally align (i.e., “restoring torque”). FIGS. 17A-17B and FIG. 18depict a comparison of the amount of restoring torque between a pair offirst and second magnets, for different kinds of magnet pairs. Inparticular, FIG. 17A depicts the restoring torque between first andsecond magnets located about 0.5 mm apart as a function of rotationalmisalignment, for non-focused magnets and focused magnets havinglongitudinal magnetic origins with a range of magnetic radii. Thenon-focused and focused magnets comprise N52 NdFeB magnets each having aD-shaped transverse cross-section, a diameter of 0.0675 inches, alongitudinal length of 0.25 inches, and a distance from the apex to theflat surface of the magnet of 0.044 inches. FIG. 17B depicts acomparison of restoring torque between a pair of non-focused magnets andbetween different pairs of focused magnets similar to that depicted inFIG. 17A, but FIG. 17B depicts this comparison in terms of percentageincrease in attractive force as a function of rotational misalignment.FIG. 18 depicts the restoring torque between the first and secondmagnets as a function of rotational misalignment for non-focused magnetsand focused magnets having a range of magnetic radii, when the first andsecond magnets are located about 1 mm apart.

As shown in FIGS. 17A-17B and FIG. 18, at small rotational misalignments(e.g., less than about 30 degrees), restoring torque increases withdecreasing magnetic radii of the first and second magnets. For example,as shown in FIG. 17B, when the air gap is about 0.5 mm and therotational misalignment is about 10%, the restoring torque betweenfocused magnets having magnetic radii of about zero is about 140%greater than that between non-focused magnets; the restoring torquebetween focused magnets having magnetic radii of about 0.25 mm is about119% greater than that between non-focused magnets; the restoring torquebetween focused magnets having magnetic radii of about 0.5 mm is about91% greater than that between non-focused magnets; the restoring torquebetween focused magnets having magnetic radii of about 0.75 mm is about72% greater than that between non-focused magnets; the restoring torquebetween focused magnets having magnetic radii of about 1 mm is about 60%greater than that between non-focused magnets; the restoring torquebetween focused magnets having magnetic radii of about 2 mm is about 35%greater than that between non-focused magnets; and the restoring torquebetween focused magnets having magnetic radii of about 4 mm is about 19%greater than that between non-focused magnets.

FIGS. 19A and 19B depict the percentage increase, relative tonon-focused magnets of similar dimension, in restoring torque between apair of focused magnets as a function of the rotational misalignmentbetween the two magnets, for a range of “air gap” distances between thefirst and second magnets. FIG. 19A depicts such a percentage increase inrestoring torque in magnets having magnetic radii of about 0.25 mm,while FIG. 19B depicts such a percentage increase in restoring torque inmagnets having magnetic radii of about 0.5 mm. As shown in FIGS. 19A and19B, for any given rotational misalignment between two focused magnets,the percentage increase in restoring torque generally increases withdecreasing “air gap” distance between the two magnets. That is, therestoring torque is greater when the two magnets are closer together.

In some variations, the first and second catheters may respectivelycomprise focused magnets, and the focused magnets may be configured suchthat restoring torque is greater than the restoring torque between twonon-focused magnets of similar dimensions and materials. This may allowthe catheters to overcome greater rotational stiffness to help bring thecatheters into rotational alignment, and may allow the restoring torquebetween the catheters to be increased when the size of the catheters(and the magnets thereof) is otherwise constrained. It may be desirableto ensure proper rotational alignment of the catheters in order topromote proper formation of the fistula using the one or more fistulaforming elements, as described above. The amount of increased restoringtorque between a pair of first and second focused magnets may depend onthe rotational alignment of the first and second magnets, the magneticradii of the first and second magnets, and/or on the distance betweenthe first and second magnets.

Magnets—Permeance Coefficient

Focused magnets may, in some instances, have a different permeancecoefficient than non-focused magnets. As a result, focused magnets mayexperience less demagnetization under various demagnetization stresses(e.g., opposing magnetic fields, elevated temperature), therebyresulting in increased magnetic flux density, or magnetic force. Thismay be particularly desirable in magnets having low intrinsiccoercivity, such as neodymium magnets (e.g., N52 magnets).

Furthermore, focused magnets may also experience less demagnetization inmagnetic domains that contribute most to generation of an attractiveforce. For example, FIG. 20A depicts the transverse cross-sections oftwo opposing non-focused D-shaped N52 magnets (2001) and (2003) havingparallel magnetic flux vectors. FIG. 20B depicts the transversecross-sections of two opposing focused D-shaped N52 NdFeB magnets (2005)and (2007) having magnetization radii of about 0.25 mm and longitudinalmagnetic origins, where the magnets are separated by an air gap of about0.5 mm. In the depicted arrangement, the region of a one magnet that isclosest to the opposing magnet may make the greatest contribution to themagnetic flux density, or magnetic force, to the air gap between theopposing magnets. For example, the convex region of magnet (2001) makesthe greatest contribution to magnetic flux density in the air gapbetween magnets (2001) and (2003), while the convex region of magnet(2005) makes the greatest contribution to magnetic flux density in theair gap between magnets (2005) and (2007).

FIGS. 20A and 20B also depict demagnetization profiles of thenon-focused magnet (2001) and focused magnet (2005), respectively. Ascan be seen by comparing the demagnetization profiles of magnets (2001)and (2005), the non-focused magnet (2001) experiences a more uniformdemagnetization than the focused magnet (2005). In contrast, focusedmagnet (2005) experiences less demagnetization in its convex regionlocated closest to the opposing magnet (2007). The decreaseddemagnetization in the convex region of focused magnet (2005) mayincrease the magnetic flux density, or magnetic force, in the regionbetween the magnets (2005) and (2007). Thus, in some variations as aresult of decreased demagnetization in crucial magnet regions, the useof focused magnets in such an arrangement (such as in cathetersdescribed herein) may provide increased attractive force and restoringtorque between the magnets.

Other Magnet Configurations

It should be appreciated that the above-described trends regardingattractive force, restoring torque, and demagnetization may also besimilarly developed in focused magnets having transverse magneticorigins, and may also be similarly developed in focused magnets havingmagnetic origins comprising a single point, and/or any suitable kind ofmagnetic origin. Moreover, the above-described trends regardingattractive force, restoring torque, and demagnetization may also besimilarly developed in focused magnets having other magnet shapes anddimensions. It should further be appreciated that the above-describedtrends may also be similarly developed in a focused magnet pair in whichthe first and second focused magnets do not have the same materials ordimensions.

For example, as shown in FIG. 21, in some instances in which a firstcatheter (2101) comprises a first magnet (2103) and a second catheter(2105) comprises a second magnet (2107), the first magnet (2103) may belonger than the second magnet (2107). When the first catheter is in afirst blood vessel, and the second catheter is in a second blood vessel,the shorter second magnet may aid in bringing the first and second bloodvessels together in apposition. In particular, the attractive force ofthe longer first magnet may act upon a smaller area of the second magnetdue to the shorter length of the second magnet, which in turn mayincrease the pressure that is generated by the second magnet on the wallof the second blood vessel. This increased pressure may facilitatebetter apposition of the first and second blood vessels, such as forbetter and/or easier fistula formation. A shorter second magnet may bedesirable in a number of situations, such as when two vessels betweenwhich a fistula is intended to be formed overlap over only a shortdistance. Additionally, a shorter second magnet may be placed in an areaof a vessel having greater curvature. As another example, when a stiffersubstance (e.g., muscle, fat, fascia, cartilage, bone) exists betweenthe vessels immediately upstream or downstream of a target fistulaformation site and hampers vessel apposition around the target fistulaformation site, use of a shorter second magnet may allow a smalleravailable segment of the second vessel to be deflected toward the firstvessel for fistula formation.

Although the focused magnets discussed above may be characterized bymagnetization patterns comprising magnetic flux vectors each passingthrough a single magnetic origin (e.g., a point or line), in othervariations, a similar effect with respect to attractive force, restoringtorque, and demagnetization may be achieved with magnets comprising acombination of two or more regions, where each region is individually“non-focused”—that is, the magnetic domains within each region havesubstantially parallel magnetic flux vectors. In particular, in somevariations, a focused magnet may include multiple regions, where themagnetization pattern of each region is represented by a plurality ofmagnetic flux vectors substantially oriented in parallel to each otherwithin each region, while the magnetic flux vectors of a first regionare oriented in a different direction than those in a second region.When combined in a particular manner, the “non-focused” regions of amagnet collectively provide a similar effect as a “focused” magnetdescribed above.

In some variations, two or more non-focused regions may be combined toform a magnet with an effective longitudinal magnetic origin (i.e., tocollectively approximate a focused magnet). For example, FIGS. 22B and22C illustrate D-shaped transverse cross-sections of magnets (2201) and(2203), respectively, which are similar in shape to the longitudinalmagnet (2204) depicted in FIG. 22A. In one variation, as shown in FIG.22B, magnet (2201) may comprise a first region (2205) with a firstnon-focused magnetization pattern represented by a first set of parallelmagnetic flux vectors (2209), and a second region (2207) with a secondnon-focused magnetization pattern represented by a second set ofparallel magnetic flux vectors (2211). As described from the perspectiveof FIG. 22B, the first domain (2205) may be located to the left of themidline of the transverse cross-section, and the second domain (2207)may be located to the right of the midline of the transversecross-section. The first and second sets of magnetic flux vectors (2209)and (2211) may be oriented toward the midline of the transversecross-section by angles α1 and α2, respectively, of approximately 45degrees. The components of the magnetic flux vectors (2209) and (2211)pointed upwards may at least partially augment each other, while thecomponents of the magnetic flux vectors (2209) and (2211) pointed to theright and left as may at least partially cancel each other. Accordingly,the summed effective magnetic flux density is focused near the apex ofthe magnet (2201) to form an effective longitudinal magnetic origin,similar to the focused magnets described with reference to FIGS. 2A-11B.

In another variation, as shown in FIG. 22C, a magnet (1303) may comprisefour domains: a first region (2213), a second region (2215), a thirdregion (2217), and a fourth region (2219), in order from left to rightas depicted in FIG. 22C. The first, second, third, and fourth regionshave respective non-focused magnetization patterns represented byrespective sets of parallel magnetic flux vectors (2221), (2223),(2225), and (2227). The first and fourth sets of magnetic flux vectors(2221) and (2227) are oriented toward the midline of the transversecross-section by angles α1 and α2, respectively, of approximately 45degrees. The second and third sets of magnetic flux vectors (2223) and(2225) may be directed upward toward the apex of the cross-section. Thecomponents of the magnetic flux vectors (2221) and (2227) that arepointed upwards may at least partially augment each other and mayfurther combine with the upward magnetic flux vectors (2223) and (2225),while the components of the magnetic flux vectors (2221) and (2227)pointed to the right and left may at least partially cancel each other.Accordingly, the summed effective magnetic flux density is focused nearthe apex of the magnet (2203) to form an effective longitudinal magneticorigin, similar to the focused magnets described with reference to FIGS.2A-11B.

It should be appreciated that in other variations, the magnetic fluxvectors (2209) and (2211) (in FIG. 22B) and magnetic flux vectors (2221)and (2227) (in FIG. 22C) may be oriented at any suitable angles α1 andα2 to produce an effective magnetic origin at any suitable location(e.g., a longitudinal magnetic origin with any suitable magnetizationradius). For instance, decreasing angles α1 and α2 may increase theeffective magnetization radius, while increasing angles α1 and α2 maydecrease the effective magnetization radius. Furthermore, angles α1 andα2 may be approximately equal to generate an effective magnetic originsubstantially aligned with the midline of the transverse cross-section,or angles α1 and α2 may be unequal to generate an effective magneticorigin in other locations.

In other variations, two or more non-focused regions may be combined toform a magnet with an effective transverse magnetic origin. For example,FIG. 23A depicts a magnet (2304) with a longitudinal axis and a D-shapedtransverse cross-section. FIG. 23B depicts a longitudinal cross-sectionof the magnet (2304). Magnet (2304) may comprise a first region (2331),a second region (2333), and a third region (2335). The first, second,and third regions have non-focused magnetization patterns represented byfirst, second, and third sets of parallel magnetic flux vectors (2337),(2339), and (2341), respectively. The first and third sets of magneticflux vectors (2337) and (2341) may be oriented toward the midline of thelongitudinal cross-section by angles α1 and α2, respectively, ofapproximately 45 degrees. The components of the magnetic flux vectors(2337) and (2341) that are pointed upwards as depicted in FIG. 23B mayat least partially augment each other and may combine with the upwardmagnetic flux vectors (2339), while the components of the magnetic fluxvectors (2337) pointing right and the components of the magnetic fluxvectors (2341) pointing left, as depicted in FIG. 23B, may at leastpartially cancel each other. Accordingly, the summed effective magneticflux density is focused so as to form an effective transverse magneticorigin, similar to the focused magnets described with reference to FIGS.12A and 12B. It should be appreciated that in other variations, themagnetic flux vectors (2337) and (2341) may be oriented at any suitableangles α1 and α2 to produce an effective magnetic origin at any suitablelocation (e.g., a transverse magnetic origin with any suitablemagnetization radius). For instance, decreasing angles α1 and α2 mayincrease the effective magnetization radius, while increasing angles α1and α2 may decrease the effective magnetization radius. Furthermore,angles α1 and α2 may be approximately equal to generate an effectivemagnetic origin substantially aligned with the midline of thelongitudinal cross-section, or angles α1 and α2 may be unequal togenerate an effective magnetic origin in other locations.

In yet other variations, the principles described with reference toFIGS. 22A-22C and FIGS. 23A-23B may be combined in any suitable manner,such that a magnet with two or more domains has an effective magneticorigin in the form of a single point, or any suitable line. For example,multiple “non-focused” regions may be combined in such a manner that theresulting magnet may have an effective magnetic origin that is somewherebetween a longitudinal magnetic origin and a transverse magnetic origin.

In some variations, the multiple non-focused regions may be formed in asingle magnet by applying a desired magnetic field to different regionsof pressed powder, as described in further detail below. In othervariations, the multiple non-focused regions may be embodied inseparately-formed magnets that are subsequently bonded or otherwisecombined together, such as through epoxy or fit together within anexternal case or shrink wrap. For example, with reference to FIG. 22B, afirst region (2205) may be embodied in a first non-focused magnet havinga half D-shaped cross-section, and a second region (2207) may beembodied in a second non-focused magnet having a half D-shapedcross-section. The first and second non-focused magnets may be combinedto form a larger magnet with an approximately D-shaped transversecross-section as shown in FIG. 22B, such as through epoxy or by fittingboth non-focused magnets into a casing having a semi-circularcross-section. Other suitable shapes of separate non-focused magnets,such as those depicted in FIG. 22C or 23A-23B or other suitable magnetshapes and sizes, may similarly be combined to form a larger magnet.

In some variations, such as shown in FIG. 24, a first catheter (2443)such as described above may comprise a magnet similar to that depictedin FIG. 23B, while a second catheter (2445) as described above maycomprise a shorter magnet (2447) having parallel magnetic flux vectors(2449) oriented in the same direction as magnetic flux vectors (2439) ina region of first catheter (2443). This arrangement may have similareffects as described above with respect to the catheter and magnet pairsof FIG. 21. It should be appreciated that while FIGS. 22A-24 depictmagnets comprising two, four, and three non-focused regions,respectively, in other variations magnets as described herein maycomprise any suitable number of regions (e.g., two, three, four, five,six, or more regions).

It should be appreciated that although in some variations the magnetsdiscussed above have been described as pairs, a catheter system mayutilize any combination of magnets as described here. For example, whenthe systems described here comprise a first catheter and a secondcatheter, either the first and/or second catheter may have more than onemagnet, which may comprise any combination of the magnets describedhere, as described in more detail above.

Systems

Also described here are systems for forming a fistula between two bloodvessels. Generally, the systems may comprise a first catheter, which maycomprise one or more fistula-forming elements and one or more magnets.The first catheter may comprise any one or more of any of thefistula-forming elements or combination of fistula-forming elements asdescribed in more detail above and in U.S. patent application Ser. No.13/298,169, which was previously incorporated by reference in itsentirety. The first catheter may comprise one or more magnets, which maybe any of the magnets described in more detail above. The first cathetermay comprise any suitable catheter body and may comprise one or moreother elements, such as one or more shape-changing elements or balloonssuch as described in more detail in U.S. patent application Ser. No.13/298,169, which was previously incorporated by reference in itsentirety.

The systems described here may also comprise a second catheter. In somevariations, the second catheter may comprise a fistula-forming elementand one or more magnets, but need not. In variations where the secondcatheter does comprise a fistula-forming element, the second cathetermay comprise any one or more of any of the fistula-forming elements orcombination of fistula-forming elements as described in more detailabove and in U.S. patent application Ser. No. 13/298,169, which waspreviously incorporated by reference in its entirety. Thefistula-forming element of the second catheter may be the same as ordifferent from the fistula-forming element of the first catheter. Thesecond catheter may comprise one or more magnets, which may be any ofthe magnets described in more detail above. The second catheter maycomprise any suitable catheter body and may comprise one or more otherelements, such as one or more shape-changing elements or balloons suchas described in more detail in U.S. patent application Ser. No.13/298,169, which was previously incorporated by reference in itsentirety.

Methods

Methods of Manufacture

Also described here are methods for manufacturing magnets withspecialized magnetization patterns, each magnetization patterncomprising a plurality of magnetic domains, where each magnetic domainis represented by a magnetic flux vector that passes through a commonmagnetic origin (e.g., a point or line). In some instances, the magnetsdescribed here may be manufactured by compressing a powder in a diewhile applying a magnetic field to the powder. The applied magneticfield may match the desired orientation of the magnetic flux vector ateach magnetic domain and cause each particle of the powder to elongateeither parallel or perpendicular to the orientation of the appliedmagnetic field. The desired applied magnetic field shape may be createdby placing the powder within a magnetically permeable fixture, whichdirects the field in the desired shape through the powder.

The fixture may comprise a highly permeable alloy, such as Hyperco 50.In other variations, the magnets may comprise isotropic magnets (e.g.,bonded neodymium or bonded samarium-cobalt magnets), which may bemagnetized in any orientation without being premagnetized in thedirection of the desired magnetic flux vectors as described above. FIG.25A depicts a transverse cross-section of a magnet (2501), a fixture(2503), and two coils (2505) and (2507) that may be used to generate themagnetic flux. As shown, the fixture (2503) may contact the magnet(2501) at three points (A), (B), and (C) around the magnet's outersurface. FIG. 25B depicts the resulting magnetic flux directed throughthe magnet (2501).

The resulting magnetization radius (i.e., the location of the magneticorigin) of the magnet is determined by the relationship between thefixture contact points and the magnet. In particular, changing thelocation of the three points around the magnet's outer surface maychange the resulting magnetization radius of the magnet. For example,moving the left and right contact points downward as depicted in FIGS.25A-25B (i.e., to wrap around the corners of the magnet (2501) tocontact the flat face of the magnet) may change the magnetization radiusof the magnet (2501).

Methods of Creating a Fistula

Also described here are methods for creating a fistula between two bloodvessels. The two blood vessels may be two closely-associated bloodvessels, such as a vein and an artery, two veins, etc. Generally, inthese methods, catheters comprising magnets as described above may beused to bring the two vessels toward each other. After the vessels arebrought toward each other, one or more fistula-forming elements may beactivated to bore through, perforate, or otherwise create a passagewaybetween the two blood vessels such that blood may flow directly betweenthe two adjoining blood vessels. When such a fistula is formed,hemostasis may be created without the need for a separate device orstructure (e.g., a suture, stent, shunt, or the like) connecting orjoining the blood vessels.

Generally, the methods described here comprise accessing a first bloodvessel with a first catheter, and advancing the first catheter to atarget location within a blood vessel. A second blood vessel may beaccessed with a second catheter, and the second catheter may be advancedto a target location within the second vessel. In some of these methods,both the first and second catheters may comprise magnets eachcharacterized by a magnetization pattern comprising magnetic fluxvectors passing through a common magnetic origin, as described in moredetail above. The first catheter may be advanced into an artery, and thesecond catheter may be advanced into a vein. In other methods, the firstcatheter may be advanced into a first vein and the second catheter maybe advanced into a second vein. In yet other methods, the first cathetermay be advanced into a first artery and the second catheter may beadvanced into a second artery. The catheters may be advanced in anysuitable manner, as described in more detail in U.S. patent applicationSer. No. 13/298,169, which was previously incorporated by reference inits entirety, and any of the catheters described in that application maybe used.

Once the first and/or second catheters have been advanced into therespective blood vessels, the catheters may be adjusted to affect thepositioning of the catheters within the blood vessels and/or thepositioning of the blood vessels relative to each other. The magnets ofthe first and second catheters may result in an attractive force betweenthe catheters, which may pull the catheters toward each other. Themagnets may also result in a torque causing the two catheters torotationally align. For example, the first and/or second catheters maycomprise one or more magnets having a magnetization pattern such asdescribed in more detail above.

Once the catheter or catheters have been positioned and adjusted, one ormore fistula-forming elements may be used to create a fistula betweenthe two blood vessels. Any of the methods for using fistula-formingelements to create one or more fistulas described in U.S. patentapplication Ser. No. 13/298,169, which was previously incorporated byreference in its entirety, may be used.

I claim:
 1. A system for creating a fistula between two vessels,comprising: a first catheter comprising a first magnet; and a secondcatheter comprising a second magnet; wherein at least one of the firstand second catheters comprises a fistula-forming element; and whereinthe first magnet is a focused magnet characterized by a firstmagnetization pattern comprising a first plurality of magnetic fluxvectors, wherein each of the first plurality of magnetic flux vectorsintersects a first magnetic origin located a first measurable distanceaway from the first magnet.
 2. The system of claim 1, wherein the firstmagnet comprises a longitudinal axis, and wherein the first magneticorigin comprises a line oriented parallel to the longitudinal axis ofthe first magnet.
 3. The system of claim 2, wherein the first magnet hasan approximately D-shaped cross-section and a longitudinal apex, whereinthe magnetic origin is offset from the longitudinal apex by betweenabout 0.25 mm and about 0.5 mm.
 4. The system of claim 1, wherein thesecond magnet is a focused magnet characterized by a secondmagnetization pattern comprising a second plurality of magnetic fluxvectors, wherein each of the second plurality of magnetic flux vectorsintersects a second magnetic origin located a second measurable distanceaway from the second magnet.
 5. The system of claim 4, wherein the firstplurality of magnetic flux vectors is directed toward the first magneticorigin and the second plurality of magnetic flux vectors is directedaway from the second magnetic origin.
 6. The system of claim 5, whereinthe first magnetic origin and the second magnetic origin at leastpartially overlap.
 7. The system of claim 4, wherein the second magnetcomprises a longitudinal axis, and wherein the second magnetic origincomprises a second line oriented parallel to the longitudinal axis ofthe second magnet.
 8. The system of claim 1, wherein the first magnetcomprises a longitudinal axis, and wherein the first magnetic origincomprises a first line oriented perpendicular to the longitudinal axisof the first magnet.
 9. The system of claim 1, wherein the first andsecond magnets are configured such that when rotational misalignmentbetween the first and second magnets is greater than about 35 degrees,an attractive force between the first and second magnets is less thanabout 50 percent of an attractive force when the rotational misalignmentbetween the first and second magnets is zero.
 10. The system of claim 1,wherein the fistula-forming element comprises an electrode.
 11. A systemfor creating a fistula between two vessels, comprising: a first cathetercomprising a first magnet, wherein the first magnet is a focused magnetcomprising a first magnetization pattern characterized at leastpartially with a first plurality of magnetic flux vectors, wherein afirst portion of the first plurality of magnetic flux vectors isoriented in a first orientation and a second portion of the firstplurality of magnetic flux vectors is oriented in a second orientationnon-parallel to the first orientation; and a second catheter comprisinga second magnet; wherein at least one of the first and second catheterscomprises a fistula-forming element.
 12. The system of claim 11, whereinthe second magnet is a focused magnet comprising a second magnetizationpattern characterized at least partially with a second plurality ofmagnetic flux vectors, wherein a first portion of the second pluralityof magnetic flux vectors is oriented in a third orientation and a secondportion of the second plurality of magnetic flux vectors is oriented ina fourth orientation non-parallel to the third orientation.
 13. Thesystem of claim 12, wherein the first and second portions of the firstplurality of magnetic flux vectors are directed toward a first commonlocus, and wherein the first and second portions of the second pluralityof magnetic flux vectors are directed away from a second common locus.14. The system of claim 13, wherein the first common locus and thesecond common locus at least partially overlap.
 15. The system of claim11, wherein the fistula-forming element comprises an electrode.